Master's Thesis

I finished Chapter 3 today, it spans 13 pages, and so I start with Chapter 5 on page 59 now. According to my time plan, I wanted page 59 to be done on Sunday, so I’m just 3 days behind. In the third chapter I mentioned factorizations of the Gabor matrices and showed what general sampling sets and the dual windows on those lattices look like, and that the duals might have a significant imaginary part. Chapter 5 will now explain Gabor expansions of images and will proceed with increasing difficulty:

• Separable atom, fully separable 4D PF-lattice (into 1D subgroups)
• Separable atom, partially non-separable PF-lattice (i.e., product of non-separable 2D lattices)
• Non-separable atom, fully separable 4D PF-lattice
• Non-separable atom on general 4D PF-lattices (only mentioned shortly)

I expect to write at least 20 pages for that chapter, they might become 30, and so I should have finished everything by the mid of October, where I want to go on a 2-week holiday while HGFei reads through my thesis. After that I just want to do cosmetic changes (minor corrections, appendix, preface) and have it printed by the beginning of November. About one month later I want to take the Master exam.

HGFei currently wants me to deal with the topic of down-/upsampling, but I’m not sure yet to what extent I’ll follow that.

I managed to finish Chapter 4 today and will continue with Chapter 3 about finite discrete GA tomorrow. Sure, this might not be done within one week as hoped, and one could think that I’m out of my time plan, but I included the sections about the 4D STFT of 2D signals and (non-)separable 2D windows, what I originally had intended for Chapter 5. The chapter spans 21 pages, and so I’m effectively on page 45 of my thesis.